Is there a way I could mirror vertex weight data to the opposite side of the mesh? e.g. from left arm to the right arm?
Maybe you are talking about this method but I don't know if there's another one. Let say you want to mirror the left arm group to the right.


If the right group already exists (because you've parented With Automatic Weight), delete it.





Select the left group and copy it.





Now mirror that copy.





Give it the correct name, i.e. with the correct suffix. This way the bone that is supposed to control it will automatically do.